theorem
  id Seg n is even
proof
  set l=<*>the carrier of Group_of_Perm n;
  0=2 * 0 + 0;
  then
A1: (len l) mod 2=0 by NAT_D:def 2;
  Product <*> the carrier of Group_of_Perm(n)=1_Group_of_Perm(n) by GROUP_4:8;
  then
A2: idseq n=Product l by Th15;
  for i st i in dom l ex q st l.i=q & q is being_transposition;
  hence thesis by A1,A2;
end;
